[[1]}, Proposition 2.10. Restated for upper-semicontinuity] 
Let \(\mathcal {Y}\)  be a locally convex space.
A proper concave function \(f : \mathcal {Y}\rightarrow [-\infty , \infty )\)  is upper-semicontinuous on \(\mathcal {Y}\)  if and only if it is upper-semicontinuous with respect to the weak topology on \(\mathcal {Y}\) .
